The 14th Amendment is mostly thought of in terms of citizenship rights and equal protection. However section 4 of that amendment makes it quite clear that the USA refused to honor or assume any debts or obligations of the CSA. Unfortunately I don't know for certain about the period between the end of the war in 1865 and the ratification of the 14th Amendment in 1868.

Section 4. The validity of the public debt of the United States, authorized by law, including debts incurred for payment of pensions and bounties for services in suppressing insurrection or rebellion, shall not be questioned. But neither the United States nor any State shall assume or pay any debt or obligation incurred in aid of insurrection or rebellion against the United States, or any claim for the loss or emancipation of any slave; but all such debts, obligations and claims shall be held illegal and void. [emphasis added]

No. As a matter of law, secession was an illegal revolt, and the debts incurred by the Confederacy were not taken on after the end of the War. See Texas v. White, 74 U.S. 700 (1869)(holding that bonds sold by secessionist state governments would not be honored).

As /u/happyatavism has noted, the Fourteenth Amendment, section 4, bars both the federal government and the states from assuming the debts of the Confederacy.